A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

0, 2, 3, 9, 11, 18, 74, 131, 144, 161, 224, 282, 390, 398, 614, 791, 1313, 1866, 9708, 10544, 13292, 13394, 29703, 30779, 72446

Offset: 1

Author

Robert Price, Apr 14 2015

Keywords

• more
• hard
• nonn

Comments

Also, numbers k such that (646*10^k - 7)/9 is prime.

Terms from Kamada.

a(26) > 10^5. Robert Price, Jul 31 2016

Examples

			For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
a(1)=0 associated with 71, a(2)=2 associated with 7177, a(3)=3 associated with 71777, a(4)=9 associated with 71777777777, etc. - _Robert Price_, Jul 31 2016
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 717w.
• Index entries for primes involving repunits.

Crossrefs

Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

Magma

[n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // Vincenzo Librandi, Apr 15 2015

Mathematica

Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]

PARI

for(n=0,200,if(isprime((646*10^n-7)/9),print1(n,", "))) \\ Derek Orr, Apr 14 2015

Extensions

a(25) from Robert Price, Jul 31 2016